Lectures related to Lie Algebras and Representations

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers the complete reducibility of complex representations and the relation between Lie algebras and Lie groups.

Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Explores Lie groups, scalar fields, and vector spaces transformations.

Explores the Kirillov paradigm for the Heisenberg group and unitary representations.

Covers Lie algebra, group representations, symmetry groups, and Schur's lemma in the context of symmetry and group operations.

Covers the representation of Lorentz transformations through general fields and the consequences of symmetry.

Covers Lie groups, Lorentz transformations, boosts, rotations, and complexified Lie algebras.

Explores simple models, electronic structure evaluation, and machine learning at the atomic scale.

Covers singular vectors in Liouville CFT, focusing on representation theory and their implications in mathematical physics.

Explores the Lie theorem and irreducible representations in group theory.

Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.